Land-atmosphere interactions play a central role in the mesoscale evolution of hydrologic fields like rainfall and soil moisture. A water balance model, capturing the essence of such interaction and driven by mesoscale and synoptic processes, was found to self-organize into states showing global scaling features both in space and in time, which we also observed experimentally. Although driving synoptic mechanisms are crucial, a key role was found for the local dynamical rules through which the system self-organizes. The results suggest the possibility of a dynamic origin for the space-time scaling in precipitation from purely local dynamics and may have implications for modeling efforts which involve land-atmosphere interaction.